Strong and electroweak interactions and their unification with non-commutative space-time

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2003-06, Vol.28 (4), p.557-560
• Main Author: He, X.-G.
• Format: Article
• Language: English
• Subjects: Bosons; Electroweak interactions (field theory); Electroweak model; Fermions; Higgs bosons; Phenomenology; Quantum theory; Spacetime
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s2003-01185-5

Quantum field theories based on non-commutative space-time (NCQFT) have been extensively studied recently. However no NCQFT model which can uniquely describe the strong and electroweak interactions has been constructed. This prevents one to make a consistent and systematic study of non-commutative space-time. In this work we construct a NCQFT model based on the trinification gauge group \(SU(3)_C\times SU(3)_{{L}}\times SU(3)_{R}\). A unique feature of this model, that all matter fields (fermions and Higgs bosons) are assigned to (anti-) fundamental representations of the factor SU(3) groups, allows us to construct a NCQFT model for strong and electroweak interactions and their unification without ambiguities. This model provides an example which allows one to make a consistent and systematic study of non-commutative space-time phenomenology. We also comment on some related issues regarding extensions to E6 and \(U(3)_C\times U(3)_{L}\times U(3)_{R}\) models.